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matics in a decade than was accomplished in a century of anti-
quity, the Middle Ages, or the late renaissance. More good
minds attack an outstanding scientific or mathematical problem
to-day than ever before, and finality has become the private
property of fundamentalists. Not one of the finalities in
Russell's remarks of 1901 has survived. A quarter of a century
ago those who were unable to see the great light which the
prophets assured them was blazing overhead like the noonday
sun in a midnight sky were called merely stupid. To-day for
every competent expert on the side of the prophets there is an
equally competent and opposite expert against them. If there
is stupidity anywhere it is so evenly distributed that it has
ceased to be a mark of distinction. We are entering a new era,
one of doubt and decent humility.
On the doubtful side about the same time (1905) we find
Poincare. '1 have spoken ... of our need to return continually
to the first principles of our science, and of the advantages GŁ
this for the study of the human mind. This need has inspired
two enterprises which have assumed a very prominent place in
the most recent development of mathematics. The first is
Cantorism. ..* Cantor introduced into science a new way of
considering the mathematical infinite ... but it has come about
that we have encountered certain paradoxes, certain apparent
contradictions that would have delighted Zeno the Eleatic and
the school of Megara. So each must seek the remedy, I for my
part - and I am not alone - think that the important thing is
never to introduce entities not completely definable in a finite
number of words. Whatever be the cure adopted, we may pro-
mise ourselves the joy of the physician called m to treat a
beautiful pathologic case.*
A few years later Poineare's interest in pathology for its own
sake had abated somewhat. At the International Mathematical
Congress of 1908 at Home, the satiated physician delivered
himself of this prognosis: 'Later generations will regard 3f engen-
khre as a disease from which one has recovered,'
It was Cantor's greatest merit to have discovered in spite of
himself and against his own wishes in the matter that the 'body
tnathematic' is profoundly diseased and that the sickness with